qed.
*)
-axiom tps_conf_subst_subst_lt: ∀L,K1,V1,W1,T1,i1,d,e,T2,K2,V2,W2,i2.
+axiom tps_conf_subst_subst_lt: ∀L,K1,V1,T1,i1,d,e,T2,K2,V2,i2.
↓[O, i1] L ≡ K1. 𝕓{Abbr} V1 → ↓[O, i2] L≡ K2. 𝕓{Abbr} V2 →
- K1 ⊢ V1 [O, d + e - i1 - 1] ≫ W1 → K2 ⊢ V2 [O, d + e - i2 - 1] ≫ W2 →
- ↑[O, i1 + 1] W1 ≡ T1 → ↑[O, i2 + 1] W2 ≡ T2 →
+ ↑[O, i1 + 1] V1 ≡ T1 → ↑[O, i2 + 1] V2 ≡ T2 →
d ≤ i1 → i1 < d + e → d ≤ i2 → i2 < d + e → i1 < i2 →
∃∃T. L ⊢ T1 [d, e] ≫ T & L ⊢ T2 [d, e] ≫ T.
(*
-#L #K1 #V1 #W1 #T1 #i1 #d #e #T2 #K2 #V2 #W2 #i2
+#L #K1 #V1 #T1 #i1 #d #e #T2 #K2 #V2 #i2
#HLK1 #HLK2 #HVW1 #HVW2 #HWT1 #HWT2 #Hdi1 #Hi1de #Hdi2 #Hi2de #Hi12
*)
#L #T0 #T1 #d #e #H elim H -H L T0 T1 d e
[ /2/
| /2/
-| #L #K1 #V1 #W1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVW1 #HWT1 #IHVW1 #T2 #H
+| #L #K1 #V1 #T1 #i1 #d #e #Hdi1 #Hi1de #HLK1 #HVT1 #T2 #H
elim (tps_inv_lref1 … H) -H
- [ -IHVW1 #HX destruct -T2
- @ex2_1_intro [2: // | skip ] /2 width=6/ (**) (* /3 width=9/ is slow *)
- | * #K2 #V2 #W2 #i2 #Hdi2 #Hi2de #HLK2 #HVW2 #HWT2
+ [ #HX destruct -T2 /4/
+ | * #K2 #V2 #i2 #Hdi2 #Hi2de #HLK2 #HVT2
elim (lt_or_eq_or_gt i1 i2) #Hi12
- [ @tps_conf_subst_subst_lt /width=19/
- | -HVW1; destruct -i2;
- lapply (transitive_le ? ? (i1 + 1) Hdi2 ?) -Hdi2 // #Hdi2
- lapply (drop_mono … HLK1 … HLK2) -HLK1 Hdi1 Hi1de #H destruct -V1 K1;
- elim (IHVW1 … HVW2) -IHVW1 HVW2 #W #HW1 #HW2
- lapply (drop_fwd_drop2 … HLK2) -HLK2 #HLK2
- elim (lift_total W 0 (i1 + 1)) #T #HWT
- lapply (tps_lift_ge … HW1 … HLK2 HWT1 HWT ?) -HW1 HWT1 //
- lapply (tps_lift_ge … HW2 … HLK2 HWT2 HWT ?) -HW2 HWT2 HLK2 HWT // normalize #HT2 #HT1
- lapply (tps_weak … HT1 d e ? ?) -HT1 [ >arith_i2 // | // ]
- lapply (tps_weak … HT2 d e ? ?) -HT2 [ >arith_i2 // | // ]
- /2/
- | @ex2_1_comm @tps_conf_subst_subst_lt /width=19/
+ [ @tps_conf_subst_subst_lt /width=15/
+ | -Hdi2 Hi2de; destruct -i2;
+ lapply (drop_mono … HLK1 … HLK2) -HLK1 #H destruct -V1 K1
+ >(lift_mono … HVT1 … HVT2) -HVT1 /2/
+ | @ex2_1_comm @tps_conf_subst_subst_lt /width=15/
]
]
| #L #I #V0 #V1 #T0 #T1 #d #e #_ #_ #IHV01 #IHT01 #X #HX